from manim import *



class math1(MovingCameraScene):
    def construct(self):
        self.camera.background_color = BLACK  # 设置背景颜色
        self.camera.frame_width = 100  # 设置边框宽度
        self.camera.frame_height = 60  # 设置边框高度
        self.camera.pixel_height = 1080  # 设置像素高度
        self.camera.pixel_width = 1920  # 设置像素宽度
        self.camera.center = ORIGIN  # 设置中心点位置
        self.camera.scale_factor = 1.0  # 设置缩放因子
        #设置横线
        for i in range(60*2+1):       
            dot1=Dot([-500,5*(i-60),0]).set_opacity(0.5)
            dot2=Dot([500,5*(i-60),0]).set_opacity(0.5)
            if i==6:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
                
            else:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
               
            self.add(dot1,dot2,line1)
        #设置竖线
        for i in range(100*2+1):        
            dot3=Dot([(i-100)*5,-300,0]).set_opacity(0.5)
            dot4=Dot([(i-100)*5,300,0]).set_opacity(0.5)
            if i==10:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
                
            else:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
            self.add(dot3,dot4,line2)
        #设置三个点
        dot1 = Dot(radius=1, color=RED)  
        dot1.move_to([-47.5,27.5,0]) 
        dot2 = Dot(radius=1, color=YELLOW)  
        dot2.move_to([-42.5,27.5,0])  
        dot3 = Dot(radius=1, color=GREEN)  
        dot3.move_to([-37.5,27.5,0])
        #镜头跟进效果 
        self.camera.frame.save_state()
        #题目出现
        self.play(self.camera.frame.animate.scale(1.2).move_to([0,-5,0]))
        text = Tex(r"\text{设}$z=f\left( x,y\right) $\text{满足}$f\left( x,0\right) =x,f\left( 0,y\right) =y^{2},f_{xy}^{''}\left( x,y\right) =x+y$\text{求}$f\left( x,y\right) $"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,20,0])
        text1 = Tex(r"\text{解:}$f_{x}'\left( x,y\right) =\int \left( x+y\right) dy=xy+\dfrac{1}{2}y^{2}+g\left( x\right) $",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,10,0])
        text2 = Tex(r"$\Rightarrow f\left( x,y\right) =\int \left( xy+\dfrac{1}{2}y^{2}+g\left( x\right) \right) dx=\dfrac{1}{2}x^{2}y+\dfrac{1}{2}xy^{2}+\int _{0}^{x}g\left( t\right) dt+\varphi \left( y\right) $",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,0,0])
        text3 = Tex(r"\text{令}$y=0\Rightarrow f\left( x,0\right) =\int _{0}^{x}g\left( t\right) dt+\varphi \left( 0\right) =x$",color=BLUE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,-10,0])
        text4 = Tex(r"\text{令}$x=0\Rightarrow f\left( 0,y\right) =\varphi \left( y\right) =y^{2}\Rightarrow \varphi \left( 0\right) =0\Rightarrow \int _{0}^{x}g\left( t\right) dt=x$",color=BLUE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,-20,0])
        text5 = Tex(r"$\Rightarrow f\left( x,y\right) =\dfrac{1}{2}x^{2}y+\dfrac{1}{2}xy^{2}+x+y^{2}$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,-30,0])





        
        self.play(Create(text),Create(text1),Create(text2),Create(text3),Create(text4),Create(text5))
        #镜头拉回
          #分析文本
        #text100=MarkupText("<b><i>分析/解：</i></b>",color=PINK).scale(5.0).move_to([-38,12.5,0])
        self.play(FadeIn(dot1),run_time=0.1)
        self.play(FadeIn(dot2),run_time=0.1)
        self.play(FadeIn(dot3),run_time=0.1)
        #题目向上移动
       
        self.wait()